The Rate and Equilibrium Constants for the Reaction NO3• + Cl- NO3

The rate and equilibrium constants for the reaction NO3• + Cl- ⇄ NO3- + Cl• in aqueous solutions were measured by pulse radiolysis. The formatio...
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1964

J. Phys. Chem. A 2003, 107, 1964-1970

The Rate and Equilibrium Constants for the Reaction NO3• + Cl- a NO3- + Cl• in Aqueous Solutions G. A. Poskrebyshev,† R. E. Huie,* and P. Neta Physical and Chemical Properties DiVision, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8381 ReceiVed: July 9, 2002; In Final Form: October 22, 2002

The rate and equilibrium constants for the reaction NO3• + Cl- a NO3- + Cl• in aqueous solutions were measured by pulse radiolysis. The formation and decay of the nitrate radical, NO3•, and the dichloride radical anion, Cl2•-, in irradiated aqueous solutions containing nitric acid and chloride ions were followed under various conditions. Because of the complexity of the system, the forward rate constant and the equilibrium constant were derived from modeling the experimental results, including secondary formation and decay reactions. The modeling study results in an equilibrium constant of Keq ) (3.5 ( 0.5) at an ionic strength between 0.1 and 1 mol L-1 and a forward rate constant k1 ) (3.5 ( 0.5) × 108 L mol-1 s-1. In contrast with previous reports, no effect of ionic strength (up to 2 mol L-1) on the forward rate constant was observed.

Introduction •,

The nitrate radical, NO3 is the most important radical in the atmosphere at night. It is formed by the reaction of nitrogen dioxide with ozone and exists in equilibrium with dinitrogen pentoxide.1 The NO3• radical is a very strong oxidant; thus, the chemistry of NO3• in the aqueous phase of the atmosphere may involve reactions with water as well as reactions with the other constituents of the solution, such as Cl-, HSO3-, FeII, or MnII. Because of the relatively high chloride ion concentration in marine clouds and aerosols, the reaction

NO3• + Cl- a NO3- + Cl•

(1) log k ) log ko -

•-,

that leads to formation of the less reactive radical, Cl2

Cl• + Cl- a Cl2•-

(2)

and then to molecular chlorine,

2Cl2•- f Cl2 + 2Cl-

The experimental indication that the kinetics of reactions involving the neutral radical NO3• is significantly affected by ionic strength, even for reactions with neutral molecules,6 is of great importance to chemical kinetics. Although the role of ionic strength in reactions of neutral species has been known for some time,7 the magnitude of the effect has generally been thought to be far less than the effect of ionic strength on reactions of ions. Essentially, this effect arises from the second term in the expanded Debye-Hu¨ckel relationship for the activity coefficient, which leads to the following expression for the rate constant at any ionic strength:

(3)

-zazbAxµ 1 + Baxµ

+ Cµ

(4)

where ko is the rate constant at zero ionic strength, µ is the ionic strength, A and B are collections of physical constants, a is the distance of closest approach, and C is an unknown constant. The other two parameters, za and zb, are the charges on the reactants thus, when za or zb ) 0:

log k ) log ko + Cµ

(5)

is of particular interest. There have been several determinations of the rate constant for the forward reaction 1 at room temperature.2-5 The rate constant values reported for this important reaction vary by a factor of 36. It was suggested that this variation is due to a strong ionic strength dependence for the reaction.4,6 More recent work indicated that the ionic strength dependence is less important, but still significant.5 In that work, the rate constant for the reverse reaction -1 was determined by generating chlorine atoms through the flash photolysis of chloroacetone in the presence of nitrate. A rate constant of k-1 ) (1.02 ( 0.04) × 108 L mol-1 s-1 was reported.

and the logarithm of the rate constant is expected to show a linear dependence on the ionic strength. Although the parameters A and B can be calculated, and a estimated, there is no reliable method of calculating C, which must be determined by experiment. Kinetic studies on many different ion-ion reactions have demonstrated that for low to moderate ionic strengths, µ < 0.1 mol L-1, the rate constant is proportional to xµ, indicating that A . C.8 Indeed, a study of the influence of ionic strength on the reaction

* Corresponding author. † On leave from the Institute of Energy Problems of Chemical Physics, Russian Academy of Sciences, Moscow 117829, Russia.

showed a very good fit with C ) 0 up to µ ) 0.4 mol L-1.9 Thus, it was surprising to see that the reaction of NO3• with

SO4•- + Cl- f SO42- + Cl•

10.1021/jp0215724 CCC: $25.00 © 2003 American Chemical Society Published on Web 03/04/2003

(6)

NO3• + Cl- a NO3- + Cl• in Aqueous Solutions

J. Phys. Chem. A, Vol. 107, No. 12, 2003 1965

Cl- showed an ionic strength effect about half that determined for the reaction of SO4•- with Cl- up to µ ) 0.4 mol L-1.6 The present study was also prompted by our recent results on the reaction of •OH radicals with nitric acid,10 •

OH + HNO3 a H2O + NO3•

•

•

(7)

which lead to a value of K5 ) (2.8 ( 0.4) × 105 extrapolated to zero ionic strength. This equilibrium constant leads to a reduction potential of E°(NO3•/NO3-) ) (2.58 ( 0.02) V (see below). But the recent results of Buxton et al.5 on the reaction of NO3• with Cl- suggest a potential about 0.1 V lower. Because of the great importance of reaction 1 in atmospheric droplets and the considerable impact of a nonnegligible effect of ionic strength on reactions of neutral radicals, we have undertaken a re-determination of the rate constant of this reaction by pulse radiolysis. In the present study, we derive the forward rate constant by kinetic techniques and also derive the equilibrium constant from the transient absorbance of the radicals. Computer modeling is utilized to analyze the experimental results in order to take into account secondary radical reactions. Experimental Section11 The NO3• radicals and Cl• atoms were generated by reaction of nitric acid and chloride ions with •OH radicals in irradiated aqueous solutions. The formation and decay of the absorbing species were followed by kinetic spectrophotometric pulse radiolysis. Fresh solutions were prepared with analytical grade HNO3 (Fluka), NaNO3 (Alfa), and NaCl (Mallinckrodt); HClO4 (Mallinckrodt) was used to increase the acidity and NaClO4 (Fluka) to increase the ionic strength. Water was purified with a Millipore Super-Q system. The solutions were deoxygenated by bubbling with ultrahigh purity nitrogen. Electron pulses from a Varian linear accelerator, with a pulse duration generally between 0.1 and 1 µs, provided doses in the range of 3 to 30 Gy, producing •OH radicals at concentrations of 2 to 18 µmol L-1. The irradiation zone was masked to 1 cm, significantly smaller than the radiation beam width, to achieve uniform radical concentration throughout the monitored solution volume. The total concentration of radicals ([•OH]o ) [•OH] + [NO3•]) formed in nitric acid solutions (0.1 e [NO3-] e 1 mol L-1) was determined by adding 1 mmol L-1 SCN- and measuring the yield of (SCN)2•-, taking a molar absorption coefficient ((SCN)2•-) ) 7580 L mol-1 cm-1 at λ ) 472 nm.12 The NO3• radical was monitored at 641 nm and the Cl2•- radical was monitored at 340 nm (see below). The kinetics of NO3• and Cl2•- formation and decay were investigated at different concentrations of chloride (from 5 × 10-5 to 4 × 10-3 mol L-1) and nitric acid (from 0.1 to 1.0 mol L-1). All experiments were carried out at room temperature, (20 ( 2) °C. Results The following primary species are produced in irradiated water:

H2O ' •OH, •H, eaq-, H+, H2O2, H2

and chloride ions, the hydroxyl radicals react with HNO3 or with Cl-,

(8)

For high-energy electron irradiation of dilute solutions, the primary radiation yields are: G(eaq-) ) 0.28 µmol J-1, G(•OH) ) 0.28 µmol J-1, G(•H) ) 0.06 µmol J-1, and G(H2O2) ) 0.075 µmol J-1.13 In N2-saturated solutions containing nitric acid

OH + HNO3 a H2O + NO3•

(7)

OH + Cl- a •ClOH- (+ H+ f Cl• + H2O)

(9)

the solvated electrons react very rapidly with NO3- and with H+,

eaq- + NO3- f NO3•2- (+ H+ f NO2• + OH-) (10) eaq- + H+ f •H

(11)

and the •H atoms react with NO3-: •

H + NO3- + H+ f NO2• + H2O

(12)

Thus several radicals are produced in this system, which engage in various subsequent reactions, leading to a complex chemical system. Because of this complexity, an accurate value of the equilibrium constant for reaction 1 cannot be determined simply from the absorbance at equilibrium or from the kinetics of approach to equilibrium. Similarly, accurate kinetics cannot be determined simply from the rates of decay or formation of NO3• and Cl2•- radicals because of the contributions of competing reactions. Computer modeling is necessary to take into account all of these competing reactions. The Molar Absorption Coefficient of the Dichloride Radical Anion. The determination of the kinetics for reaction 1 by modeling requires that we know the absolute concentrations of both NO3• and Cl2•-. We use the molar absorption coefficient of the NO3• radical determined in this laboratory,10 (NO3•)641 ) (1130 ( 50) L mol-1 cm-1 and (NO3•)340 ≈ 390 L mol-1 cm-1. We have re-determined the value for Cl2•-. This latter value was measured at 340 and 350 nm by pulse irradiating aqueous solutions at pH 1 which contained either NaCl (2.5 × 10-2 mol L-1) or KSCN (1 × 10-2 mol L-1). The pH was adjusted with HClO4 in both cases and the solutions were pulse irradiated both under air and after purging with nitrogen. By assuming that the yield of Cl2•- is equal to the yield of (SCN)2•-, we determined (Cl2•-)340 ) (8800 ( 650) L mol-1 cm-1 and (Cl2•-)350 ) (8450 ( 630) L mol-1 cm-1. Our value is identical with that reported by Jayson et al.14 at 340 nm and we agree very closely with the value of 8600 L mol-1 cm-1 at 345 nm reported by Kim and Hamill.2 Our result is somewhat higher than the value of Lierse et al.15 of 8100 L mol-1 cm-1 and lower than the value of Adams et al.16 of 9600 L mol-1 cm-1, both at 340 nm. In addition, we determined (Cl2•-)641 e 90 L mol-1 cm-1. Experimental Results on Equilibrium 1. The following experimental results point to the existence of equilibrium 1. Figure 1 shows representative kinetic traces at various concentrations of HNO3 and Cl- monitored by absorbance at 641 nm and at 340 nm. These follow the formation and decay of the NO3• and Cl2•- radicals, respectively. In all cases, the absorbance at these wavelengths increases to a maximum and then decreases to zero. For the discussion below, we define Amax as the maximum absorbance in the kinetic trace, corresponding to a maximum in the concentration of the radical being monitored. The time at which Amax is reached is different for the two wavelengths, indicating that the two reactants are not merely competing for the primary oxidizing radicals but rather that the chlorine species is formed at least in part by reaction 1. From these and other traces we find that Amax at 641 nm increases

1966 J. Phys. Chem. A, Vol. 107, No. 12, 2003

Poskrebyshev et al.

Figure 1. Kinetic traces for the formation and decay of the NO3• radical, monitored at 641 nm (left), and the Cl2•- radical, monitored at 340 nm (right), following pulse irradiation of deoxygenated aqueous solutions containing various concentrations of nitric acid and chloride ions: (a) 0.2 mol L-1 HNO3, 3 mmol L-1 Cl-; (b) 0.4 mol L-1 HNO3, 2 mmol L-1 Cl-; (c) 1.0 mol L-1 HNO3, 1 mmol L-1 Cl-; (d) 1.0 mol L-1 HNO3, 2 mmol L-1 Cl-; (e) 1.0 mol L-1 HNO3, 4 mmol L-1 Cl-. The curves were calculated by modeling the reactions given in Table 1 (see text for details).

with an increase in [HNO3] but decreases with an increase in [Cl-] (Figure 2). Inversely, Amax at 340 nm increases with [Cl-] but decreases with an increase in [HNO3] (Figure 3). These results point to the existence of an equilibrium reaction, although due to loss processes, the values of Amax do not represent this equilibrium alone. An increase in the concentration of Cl- leads to a more rapid and more complete reaction of NO3• radicals with Cl- to form Cl2•-, until the concentration of the latter species approaches the initial concentration of the hydroxyl radicals, [•OH]o. Under these conditions, the decay of Cl2•- follows a second-order rate law and the rate constant was calculated to be k3 ) (2.0 ( 0.3) × 109 L mol-1 s-1, in line with most of the values reported in the literature.17 The observed formation of the absorption at 340 nm does not follow a simple first-order rate law because of the various radical-radical reactions that take place concurrently with

reaction 1. As the first step in the evaluation of the results, we approximated the experimental traces to a first-order rate (kobs). The value of kobs increases with [Cl-] but decreases with [HNO3] (Figure 4). The latter observation is due to the fact that when the concentration of nitric acid is increased, the contribution of the rapid reaction 9 is diminished compared with that of reaction 7 and the formation of Cl• is now due more to the slower reaction 1. The dependences of kobs and Amax on [Cl-] in Figures 2-4 were obtained both at pH 0 (1 mol L-1 HNO3) and at pH 0.7 (0.2 mol L-1 HNO3). Modeling Studies. To derive more accurate values for rate and equilibrium constants for reaction 1, we modeled the kinetics of formation and decay of NO3• and Cl2•-. The modeling was carried out with the kinetic scheme summarized in Table 1. The scheme includes the equilibrium reactions 1, 7, and 13; the reactions of the primary radicals with the various solutes and subsequent equilibria of the species produced, and finally, the

NO3• + Cl- a NO3- + Cl• in Aqueous Solutions

J. Phys. Chem. A, Vol. 107, No. 12, 2003 1967

Figure 2. The maximum absorbance at 641 nm (nitrate radicals) produced by a 23 Gy electron pulse (a) as a function of nitric acid concentration ([Cl-] ) 2 mmol L-1), and (b) as a function of chloride concentration ([HNO3] ) 0.2 mol L-1 (O) and 1 mol L-1 (b)).

Figure 3. The maximum absorbance at 340 nm (Cl2•- radicals) produced by a 23 Gy electron pulse (a) as a function of chloride concentration ([HNO3] ) 0.2 mol L-1 (O) and 1 mol L-1 (b)), and (b) as a function of nitrate concentration ([Cl-] ) 2 mmol L-1).

various radical-radical reactions expected in the system (reactions 3 and 16-31). Except for the rate constant for the forward reaction of NO3• with Cl- (reaction 1) the rate constants were taken from the literature where possible, including the value of k-1, which was taken from the recent paper by Buxton et al.,5 where it was measured directly by flash photolysis in the absence of Cl- ions. In addition to the known reaction of H• with NO3-, we considered the reaction of H• with HNO3, which has not been reported. If this reaction proceeds to form NO2•, it has no effect. But if the reaction proceeds by abstraction to form NO3• (reaction 14), it has a significant impact on the model output if k14 > 1 × 107 L mol-1 s-1. This value is significantly greater than the upper limit reported for this reaction in the gas phase.18 The value of k3 was determined in the present study and is identical to values reported in several earlier studies.17 Reaction 30 was introduced in order to account for the expected radicalradical reaction when both NO3• and Cl2•- are present. This reaction appears to be important in this system and although its rate constant is not known, it must be within an order of magnitude of the diffusion-controlled limit. This is expected for an electron-transfer reaction with a very high driving force (E(Cl2/Cl2•-) ) 0.70 V19 and E°(NO3•/NO3-) ) 2.48 V, see below). The value of k30 that gives the best fit to the present results is 1 × 109 L mol-1 s-1. If we choose a lower value, reaction 30 will have a minimal effect on the decay kinetics; if we choose a higher value, the calculated decay will appear to be much faster than the experimentally observed decay. In parallel with reaction 30, we introduced reaction 31 and initially assumed a similar rate constant. Reactions 30 and 31 have the same effect on the decay kinetics of Cl2•- radicals but opposite effects on the decay kinetics of NO3• radicals. From the modeling we determined that this value is an upper limit for

k31. Of the other radical-radical reactions in Table 1, the reactions of the hydroxyl radical have little effect on the model results, due, primarily, to the dominance of reactions 7 and 9. On the other hand, reactions of hydrogen atoms with other radicals have an observable effect, since the main reaction of hydrogen atoms with a molecule is reaction 12, which is slow. Reaction of Cl2•- with nitrate ions was found to have no observable effect on the modeling results. The radical formation rate during the pulse is essentially linear. For modeling purposes, we combined two exponential formation rates with rate constants such that the formation of the radicals was 90% complete within the pulse width of ≈1 µs. Figures 1-4 show the experimental results along with the curves calculated from the model (taking into account the absorbance of NO3• and Cl2•- both at 340 and 641 nm). The best fit was obtained with the value of k1 ) (3.5 ( 0.5) × 108 L mol-1 s-1. In addition, we carried out calculations setting the rate constant for reaction -7 to zero. No effect on the calculated curves was found, showing that this reaction becomes unimportant when [Cl-] g 1 × 10-3 mol L-1, as expected on the basis of the rate constants in Table 1. The effect of a change in ionic strength on this reaction system was investigated by using 0.2 mol L-1 HNO3 solutions containing Cl- at concentrations between 5 × 10-5 and 4 × 10-3 mol L-1 and adding up to 2 mol L-1 NaClO4. The kinetic traces were fitted to a first-order rate equation to obtain k′obs. Figure 5a shows the dependence of k′obs on [Cl-] and Figures 5b and 5c show typical traces in the absence and presence of 2 mol L-1 NaClO4. Within the experimental uncertainty, no effect of the ionic strength on the kinetics of decay of NO3• was observed.

1968 J. Phys. Chem. A, Vol. 107, No. 12, 2003

Poskrebyshev et al. TABLE 1: Reactions and Rate Constants Used for Modelinga reaction no.

reaction

13 -13 7 -7 1 -1 10 10a 11 12 14 9 -9 15 -15 2 -2 3 16 17 18 19 20 21 22

HNO3 f H+ + NO3H+ + NO3- f HNO3 •OH + HNO f H O + NO • 3 2 3 NO3• + H2O f HNO3 + •OH • • NO3 + Cl f NO3 + Cl NO3- + Cl• f NO3• + Cleaq- + NO3- f NO3•2NO3•2- + H+ f NO2 + OHeaq- + H+ f H• H• + NO3- f NO2• + OHH• + HNO3 f H2 + NO3• •OH + Cl- f HOCl•HOCl•- f •OH + ClHOCl•- + H+ f H2O + Cl• Cl• + H2O f HOCl•- + H+ Cl• + Cl- f Cl2•Cl2•- f Cl•+ ClCl2•- + Cl2•- f 2Cl- + Cl2 •OH + •OH f H O 2 2 H• + •OH f H2O • • H + H f H2 NO3• + NO2• f N2O5 NO2• + NO2• f N2O4 N2O4 f NO2• + NO2• N2O4 + H2O f HNO3 + HNO2 •OH + NO • f HONO or 2 2 HNO3 H• + NO2• f HNO2 NO3• + NO3• f products •OH + NO • f HONO 3 3 H• + NO3• f HNO3 Cl2•- + •OH f HOCl + ClCl2•- + H• f H+ + 2ClNO3• + Cl2•- f NO3- + Cl2 NO2• + Cl2•- f (NO2-+Cl2) or (NO2++2Cl-)

23 24 25 26 27 28 29 30 31

Figure 4. The observed rate of formation of the absorbance at 340 nm (Cl2•- radicals) (a) as a function of chloride concentration ([HNO3] ) 0.2 mol L-1 (O) and 1 mol L-1 (b)), and (b) as a function of nitrate concentration ([Cl-] ) 2 mmol L-1).

Discussion The present results indicate that the ionic strength effect is much lower than that reported previously and is probably negligible, more like the small effects noted previously for reactions of ions and neutral molecules.8 We should point out that in preliminary experiments we did detect an effect of sodium perchlorate on the rate of reaction 1. This effect vanished when we purchased a high-purity sample of the salt. We suggest that the effect of ionic strength on the kinetics of NO3• reactions that was observed before5 may be the result of impurities in the salts. The greater ionic strength effect observed in the earlier work4,21 probably indicates also additional experimental complications,5 and possibly including an effect of ionic strength on the reaction that is employed to generate NO3•. Reaction 30 may play an important role in atmospheric aerosols. It leads, along with reaction 1, to conversion of chloride ions into chlorine, which may diffuse from the acidic droplet into the gas phase and undergo UV photolysis. This reaction is similar to the known reaction between ozone and Cl2•-, for which a rate constant of 9 × 107 L mol-1 s-1 in aqueous solutions has been reported.22 Reaction 31, on the other hand, may proceed in two opposing directions, leading to oxidation or reduction of Cl2•-, and its rate constant may be significant in atmospheric modeling despite its lack of effect on the current system. Reduction Potential Calculations. The rate constant reported here, k1 ) (3.5 ( 0.5) × 108 L mol-1 s-1, can be combined with the reported rate constant for the reverse reaction, k-1 ) 1.0 × 108 L mol-1 s-1, to yield an equilibrium constant for the reaction of NO3• with Cl-, K1 ) (3.5 ( 0.5). This leads to a value for the difference between the reduction potentials of these two radicals, E°(NO3•/NO3-) - E°(Cl•/Cl-) ) 0.032 ( 0.005

k (L mol-1 s-1)

reference

2 × 1010 (s-1) (4.4 to 6.0)b × 108 (0.88 to 1.2)b × 108 3 × 102 3.5 × 108 1.0 × 108 9.7 × 109 4.5 × 1010 2.3 × 1010 4.4 × 106 e1 × 107 4.3 × 109 6.1 × 109 (s-1) 2.1 × 1010 4.5 × 103 8.5 × 109 6 × 104 (s-1) 2 × 109 5.5 × 109 7 × 109 7.8 × 109 1.0 × 109 4.7 × 108 6.8 × 103 (s-1) 1.8 × 101

5 31 32 31 33 c 14 14 14 24 24,34,35 24 d, 17 31 36 31 37 38 38 38

4.5 × 109

39

1 × 1010 4 × 106 1 × 1010 1 × 1010 1 × 1010 7 × 109 1 × 109

39 40 e e 20 15

28,29 30 10 10

e 1× 109

a

The rate constants are given in second-order units, except where noted. b Depending on ionic strength, see ref 10. c See text. d This work. e Estimated from gas-phase value.18

V. A reduction potential of E°(Cl•/Cl-) ) 2.41 V has been calculated before23 from the reduction potential E°(•OH/OH-) ) 1.89 V and the equilibrium constants for reactions 9 and 13 as determined by Jayson et al.14 By replacing the earlier value14 of k-13 with the latest value24 given in Table 1 and taking the latest recommended value19 for E°(•OH/OH-) ) 1.90 V, we calculate E°(Cl•/Cl-) ) (2.44 ( 0.01) V. This leads to E°(NO3•/ NO3-) ) (2.47 ( 0.01) V. (The indicated uncertainty does not include the uncertainty in the value for the reference couple.) In a previous study,25 we had determined E°(SO4•-/SO42-) - E°(Cl•/Cl-) ) 0.003 V at near zero ionic strength. Because of round-off above, this leads to E°(SO4•-/SO42-) ) 2.45 V. Studies of the forward and reverse reactions

SO4•- + NO3- a SO42- + NO3•

(32)

found k32 ) 5.0 × 104 L mol-1 s-1 4,26 and k-32 ) 1.0 × 105 L mol-1 s-1.26 The equilibrium constant, K32 ) 0.5 ( 0.1, leads to a reduction potential difference of 18 mV at an ionic strength of approximately 0.25 mol L-1. Correcting the forward reaction to zero ionic strength gives k32 ) 2.1 × 104 L mol-1 s-1 and K32 ) 0.21 ( 0.1. From this we obtain E°(NO3•/NO3-) E°(SO4•-/SO42-) ) 0.040 ( 0.015 V and E°(NO3•/NO3-) ) 2.49 ( 0.02 V. This value is confirmed by the less precise value of E°(NO3•/ NO3-) - E°(SO4•-/SO42-) ) 0.031 ( 0.029 V, which can be

NO3• + Cl- a NO3- + Cl• in Aqueous Solutions

J. Phys. Chem. A, Vol. 107, No. 12, 2003 1969

Figure 5. Effect of ionic strength: (a) the observed rate of decay of the absorbance at 641 nm (nitrate radicals) as a function of chloride ion concentration in 0.2 mol L-1 HNO3 solutions in the absence (O) and presence (b) of 2 mol L-1 NaClO4; (b) and (c) typical comparative traces at 1.2 and 2.5 mmol L-1 Cl-, respectively, in the absence (O) and presence (b) of 2 mol L-1 NaClO4.

derived from equilibrium measurements on the reactions

ClO3• + NO3- a ClO3- + NO3•

(33) References and Notes

and •-

SO4

-

+ ClO3 a SO4

2-

+ ClO3

•

(34)

as discussed in our previous paper.10 This leads to E°(NO3•/ NO3-) ) 2.48 ( 0.03 V. In a recent study10 we had determined the equilibrium constant for the reaction

OH + HNO3 a H2O + NO3•

•

water (to obtain a dimensionless equilibrium constant), our previous calculation had mixed different standard states and was incorrect. The correct calculation that can be based on E°(H+,•OH/ H2O) ) 2.72 V should take the rate constant of the reverse reaction in first-order units, k-7 ) (1.7 ( 0.6) × 104 s-1, and K7 ) (5.0 ( 1.5) × 103 L mol-1, to yield a reduction potential of E°(NO3•/NO3-) ) (2.58 ( 0.02) V. This corrected value is higher than the three values derived above from the various other equilibria. Those three values were based directly or indirectly on E°(Cl•/Cl-) ) (2.44 ( 0.01) V and are self-consistent at E°(NO3•/NO3-) ) (2.48 ( 0.03) V. The value of E°(NO3•/NO3-) ) (2.58 ( 0.02) V is based directly on E°(H+,•OH/H2O) ) 2.72 V. The discrepancy between these two sets of values raises doubts about the value of the equilibrium constant for the system of Cl• vs •OH or NO3• vs •OH or both. Indeed, inspection of the equilibria in Table 1 shows that K15 should be equal to K7K1/(K9K13). The values in Table 1, however, show a discrepancy of a factor of about 100, which translates to a reduction potential difference of about 0.1 V, as above. Since the rate constants for reactions of •OH radicals with nitrate and chloride ions are relatively high and have been measured with sufficient accuracy, we expect that the discrepancy in reduction potentials is due to uncertainties in the rate constants for the slow reactions of Cl• and NO3• with water. The slowness of these reactions also means that the discrepancy will have little impact on the kinetic model, since these reactions have little effect on the time history of the NO3•or Cl2•-. Literature values for the kinetics of the reactions of Cl• and NO3• with water vary widely, particularly for NO3•. Moreover, the reactions of these radicals with water may not produce •OH directly; at least for the case of Cl• the reaction has been suggested to produce an adduct which involves additional equilibria on route to formation of •OH.24,27 We believe that further measurements are necessary to reconcile the reduction potentials discussed above. In the meantime, however, because of smaller discrepancies between experimental results by various authors on the Cl systems, as compared with wider discrepancies on the •OH/NO3• system, we tentatively adopt the value of E°(NO3•/NO3-) ) (2.48 ( 0.03) V.

(7)

from the forward and reverse rate constants. The rate constants at zero ionic strength were found to be k7 ) (8.6 ( 1.3) × 107 L mol-1 s-1 and k-7 ) (3 ( 1) × 102 L mol-1 s-1, and the equilibrium constant K7 ) (2.8 ( 0.4) × 105. From the latter value of K7 and taking E°(H+,•OH/H2O) ) 2.72 V we calculated a reduction potential E°(NO3•/NO3-) ) (2.48 ( 0.01) V. In this calculation, however, we failed to notice that E°(H+,•OH/ H2O) ) 2.72 V is derived from E°(•OH/OH-) ) 1.90 V by taking Kw ) 10-14 and not taking into account the concentration of water as 55.56 mol L-1 (i.e., taking the standard state of liquid water as 1 rather than taking the activity of water). Since our value of K7 ) (2.8 ( 0.4) × 105 includes the activity of

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